21.3.2 Permutation Matrix Functions

inv and pinv will invert a permutation matrix, preserving its
specialness. det can be applied to a permutation matrix, efficiently
calculating the sign of the permutation (which is equal to the determinant).

A permutation matrix can also be returned from the built-in functions
lu and qr, if a pivoted factorization is requested.

The sparse function will convert a permutation matrix efficiently to a
sparse matrix.
The find function will also work efficiently with a permutation matrix,
making it possible to conveniently obtain the permutation indices.